Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator
Representation Theory
2009-05-27 v4 Mathematical Physics
math.MP
Abstract
Operadic Lax representations for the harmonic oscillator are used to construct the dynamical deformations of three-dimensional (3D) real Lie algebras in the Bianchi classification. It is shown that the energy conservation of the harmonic oscillator is related to the Jacobi identities of the dynamically deformed algebras. Based on this observation, it is proved that the dynamical deformations of 3D real Lie algebras in the Bianchi classification over the harmonic oscillator are Lie algebras.
Keywords
Cite
@article{arxiv.0807.0428,
title = {Dynamical deformations of three-dimensional Lie algebras in Bianchi classification over the harmonic oscillator},
author = {Eugen Paal and Jyri Virkepu},
journal= {arXiv preprint arXiv:0807.0428},
year = {2009}
}
Comments
LaTeX2e, no figures, 9 pages